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GUJCET · Physics · Alternating Current
In an AC circuit, a resistance of \(\mathbf{R}\) ohm is connected in series with an inductor of self inductance \(L\). If phase angle between voltage and current be \(45^{\circ}\), the value of inductive reactance \(\left(X_{L}\right)\) will be equal to ____________ .
- A \(\frac{\mathrm{R}}{4}\)
- B \(\frac{\mathrm{R}}{2}\)
- C R
- D \(\frac{\mathrm{R}}{8}\)
Answer & Solution
Correct Answer
(C) R
Step-by-step Solution
Detailed explanation
(C) \(R\)
\(
\begin{aligned}
\tan \delta & =\frac{\omega \mathrm{L}}{\mathrm{R}} \\
\therefore \quad \tan 45^{\circ} & =\frac{\omega \mathrm{L}}{\mathrm{R}} \\
\therefore \quad \omega \mathrm{~L} & =\mathrm{R}=\mathrm{X}_{\mathrm{L}} \\
& \left(\because \tan 45^{\circ}=1\right)
\end{aligned}
\)
\(
\begin{aligned}
\tan \delta & =\frac{\omega \mathrm{L}}{\mathrm{R}} \\
\therefore \quad \tan 45^{\circ} & =\frac{\omega \mathrm{L}}{\mathrm{R}} \\
\therefore \quad \omega \mathrm{~L} & =\mathrm{R}=\mathrm{X}_{\mathrm{L}} \\
& \left(\because \tan 45^{\circ}=1\right)
\end{aligned}
\)
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